The initial term is found through Fourier optics in conjunction with the slow varying envelope approximation considering an weighted superposition of plane waves [1]}. Due to the large refractive index of diamond, a significant spherical aberration occurs at the interface, however by applying the opposing phase to the SLM, this can be mitigated. We follow work by Jesacher et al. [2]} to separate out focal aberrations and calculate an unaberrated focal volume with a focal depth at 20 \(\mu \) m. The time dependence of the electric field was modelled as a Gaussian multiplied by a sinusoid of the laser frequency, \(\omega _0\) . The width is defined such that the full width half maximum (FWHM) of the squared Gaussian envelope is equal to the pulse duration. The spatial and time dependence's are multiplied together and the propagation of the pulse is included by an additional phase factor due to the differing phase velocities across the focal region.
\( I_0(x,y,z,t)=I_V(x,y,z) \cdot I_t\Bigg (t+\frac{\omega _0 n^2 (z_0-z)}{c^2 \phi (x,y)}\Bigg )\qquad \mathrm {(S2)}\) 
